Basic strategy Blackjack

In the game of Blackjack the player tries to play his hand the best he can to achieve a beter score-total than the bank.
In trying to do this, he is constantly faced with game decisions. Some are easy, like standing on 20 points or hitting(new card) on 7 points.
Some are more difficult: 14 points is little to stand at, but hitting can easily lead to too many points.
The result of a decision always depends on the cards that show on the table, and their exact order.
Lets assume, for example, that the player at the last box is handed two fives as first cards.
The bank has an eight. It’s the players turn, he can choose between splitting, doubling, buying or standing.
Any decision can turn out well or wrong in the given situation. Afterwards, one can always, from the cards that come out of the deck, deduce which of the four decisions would have been best.

Too bad nobody knows what cards will show up beforehand.
After all, blackjack is played with thouroughly shuffled cards.
Every card-order that shows up is therefore purely coincidential.
The idea of a perfect decision in every possible situation is a thought one has to let go.
A usefull approach however, is looking at the results for a decision, taking all possible card combinations in concideration.
One can then easily show that splitting or standing on two fives is rarely a good choice.
These exceptions are caused by strange orders in the deck which can never be predicted or seen beforehand in the game.
Therefore one can call splitting or standing in this situation a wrong decision, even if it would’ve turned out well.
Likewise, just buying a card is obviously worse than doubling.
In this manner (looking at all combinations and see what is the best option), one can determine what the best decision is for any game situation.
The strategy found in this way is called the ‘basic strategy’
The above also shows that this basic strategy can also turn out quite bad, after all, we’re dependant of the card order in the deck.
But overall, in the long term, profits will be maximal with the basic-strategy.

The basic-strategy seems to be highly dependant of the first card of the bank. This card has a very big influence on the chances of the bank.
The bank kan either buy itself dead or end with 17,18,19,20,21 points or get a ‘Black Jack’. Because the bank doesnt have the freedom of decision (buy to and on 16 points, stand from 17) bank chances can be easily calculated. Very important is the chance that the bank will buy itself dead. On average this chance is 28%. For all different first cards for the bank we find the following chances:

Kaart
bank

2

3

4

5

6

7

8

9

T

A

Kans dood (%)

35

37

40

42

42

26

24

23

21

12

This table shows that the first card of the bank can be divided into two categories:
– With small cards (2, 3,4, 5 and 6) the bank has a relatively high chance (40%) to buy itself dead;
– With large cards (7, 8, 9, T and A) the bank has a smaller probability (around 20%) to buy itself dead.
This remarkable difference in behavior between small and large cards of the first bank is caused by the rule that the bank has to buy to and on 16 and from 17 must stand, and is emphasised by the large number of tens in the deck. Without further calculations, we can now estimate the following:

– A small card in the bank is good for the player. In order to reap maximum profit from this situation, offensive gameplay is advised: split a lot, double a lot, and stand on bad hands (12-16) in the hope that the bank will buy itself dead;
– A large card in the bank is generally disadvantageous for the player. With defensive gameplay, the downside can be limited. This means don’t split, don’t double a lot and hit cards until a reasonable hand is attained.

Tables for the basic strategy

The following tables are the maps of the bank horizontally and relevant hands of the player vertically.